I have searched the forum and I didn't find the answers to my question.

My question is: is there a vertical load on the relief valve since there is pressure difference on both sides of the orifice?

Thanks,

Not an answer, just a question over your question, maybe it would be helpful.
Where exactly do you think is this "pressure border" inside the PSVs?

Hello,
I would suggest you to read the ASME 31.1 nonmandatory appendix-II. if you read the rules for safety valve installation you will get your answer. There is a pressure difference when we are using the safety valve, but there are generally two systems,
1. open dischange system
2. close dischange system.
The value of force will depend on the type of which system you are wokring with.
Regards,
RK